Ovidiu Savin and Enrico Valdinoci
Regularity of nonlocal minimal cones in dimension 2
(19K, LaTeX)

ABSTRACT.  For any $s\in(0,1)$, we consider sets of minimal $s$-perimeter
in $\R^2$. We prove that there are no $s$-minimal cones
other than the half-planes and that
all the $s$-minimal sets are locally $C^{1,lpha}$.